Recent work has shown logical background knowledge can be used in learning
systems to compensate for a lack of labeled training data. Many methods work by
creating a loss function that encodes this knowledge. However, often the logic
is discarded after training, even if it is still useful at test time. Instead,
we ensure neural network predictions satisfy the knowledge by refining the
predictions with an extra computation step. We introduce differentiable
refinement functions that find a corrected prediction close to the original
prediction. We study how to effectively and efficiently compute these
refinement functions. Using a new algorithm called Iterative Local Refinement
(ILR), we combine refinement functions to find refined predictions for logical
formulas of any complexity. ILR finds refinements on complex SAT formulas in
significantly fewer iterations and frequently finds solutions where gradient
descent can not. Finally, ILR produces competitive results in the MNIST
addition task.

本文介绍了一种基于逻辑背景知识和可微化的改进函数的学习方法，以提高神经网络在训练和测试中的预测准确性，其中涉及迭代局部细化算法及应用于 MNIST 加法任务的结果。